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Nasir al-Din Tusi

Author: Nabeela Quraishi

Nasir al-Din Tusi, was a famous Persian philosopher, scientist, and mathematician of the 13th century. Tusi was born on Feb. 18, 1201 in Ṭūs, Khorāsān, now a part of Iran. He died in Baghdad, Iraq, in the year 1274. He was born to a shi’a family and his father passed away when he was still quite young. Tusi however,  made it his lifelong endeavour to seek knowledge at an excellent level, as was his father’s wish.

Tusi’s writings amount to approximately 150  scholarly works on astronomy, ethics, history, jurisprudence, logic, mathematics, medicine, philosophy, theology, poetry and the popular sciences.

Tusi travelled far and wide in the pursuit of knowledge. He was very keen on acquiring knowledge from renowned scholars of that time. Some of the scholars who influenced his work are: Kamal al-Diin Hasib from whom he studied mathematics. While in Mawsil he studied mathematics and astronomy with Kamal al-Din Yunus.

In addition to his own scholarly work, he edited the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus, and Theodosius. He also made original contributions to mathematics and astronomy. One of Tusi’s most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. This work also contains the famous sine formula for plane triangles: a/sinA=b/sinB=c/sinC.

Another mathematical contribution was Tusi’s manuscript, dated 1265, concerning the calculation of n-th roots of an integer; In the manuscript al-Tusi determined the coefficients of the expansion of a binomial to any power giving the binomial formula and the Pascal triangle relations between binomial coefficients.

With the permission of the Mongol conqueror Hulegu Khan, Tusi built an observatory in Maragheh, a place in northwestern Iran. It had various instruments such as a 4 metre wall quadrant made from copper and an azimuth quadrant which was the invention of Al-Tusi himself.

Tusi also designed other instruments for the Observatory. Ṭusi’s most influential book in the West may have been Tadhkirah fi ʿilm al-hayʿa (“Treasury of astronomy”), which describes a geometric construction, now known as the al-Ṭūsī couple, for producing rectilinear motion from a point on one circle rolling inside another. By means of this construction, Ṭusi succeeded in reforming the Ptolemaic planetary models, producing a system in which all orbits are described by uniform circular motion.

The Tusi couple – A circle rolling inside a circle | IB Maths Resources  from Intermathematics

Most historians of Islamic astronomy believe that the planetary models developed at Marāgheh found their way to Europe (perhaps via Byzantium) and provided Nicolaus Copernicus (1473–1543) with inspiration for his astronomical models.

Tusi used his Observatory in making very accurate tables of planetary movements. He published Zij-i ilkhani (the Ilkhanic Tables), written first in Persian and later translated into Arabic, after making observations for 12 years. This work contains tables for computing the positions of the planets, and it also contains a star catalogue. He also wrote works on astronomical instruments, for example on constructing and using an astrolabe.

He wrote a famous work on minerals which contains an interesting theory of colour based on mixtures of black and white, and included chapters on jewels and perfumes. He also wrote on medicine.

These are some of the scholarly and influential works of Tusi according to subject matter: 

(1) Astronomy: al-Tadhkira fi ‘ilm al-hay’a; Zij Ilkhani; Risala-yi Mu‘iniyya and its commentary. (2) Ethics: Gushayish-nama; Akhlaq-i Muhtashami; Akhlaq-i Nasiri, ‘Deliberation 22’ in Rawda-yi taslim (3) History: Fath-i Baghdad which appears as an appendix to Tarikh-i Jahan-gushay of Juwayni (London, 1912-27), vol. 3, pp. 280-92. (4) Jurisprudence: Jawahir al-fara’id. (5) Logic: Asas al-iqtibas. (6) Mathematics: Revision of Ptolemy’s Almagest; the epistles of Theodosius, Hypsicles, Autolucus, Aristarchus, Archimedes, Menelaus, Thabit b. Qurra and Banu Musa. (7) Medicine: Ta‘liqa bar qunun-i Ibn Sina (8) Philosophy: refutation of al-Shahrastani in Musara‘at al-musari‘; his commentary on Ibn Sina’s al-Isharat wa’l-tanbihat which took him almost 20 years to complete; his autobiography Sayr wa suluk; Rawda-yi taslim and Tawalla wa tabarra. (9) Theology: Aghaz wa anjam; Risala fi al-imama and Talkhis al-muhassal and (10) Poetry: Mi‘yar al-ash‘ar.

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